Abstract
Vertebrates possess different types of retinal specializations that vary in number, size, shape, and position in the retina. This diversity in retinal configuration has been revealed through topographic maps, which show variations in neuron density across the retina. Although topographic maps of about 300 vertebrates are available, there is no method for characterizing retinal traits quantitatively. Our goal is to present a novel method to standardize information on the position of the retinal specializations and changes in retinal ganglion cell (RGC) density across the retina from published topographic maps. We measured the position of the retinal specialization using two Cartesian coordinates and the gradient in cell density by sampling ganglion cell density values along four axes (nasal, temporal, ventral, and dorsal). Using this information, along with the peak and lowest RGC densities, we conducted discriminant function analyses (DFAs) to establish if this method is sensitive to distinguish three common types of retinal specializations (fovea, area, and visual streak). The discrimination ability of the model was higher when considering terrestrial (78%–80% correct classification) and aquatic (77%–86% correct classification) species separately than together. Our method can be used in the future to test specific hypotheses on the differences in retinal morphology between retinal specializations and the association between retinal morphology and behavioral and ecological traits using comparative methods controlling for phylogenetic effects.

Introduction

The vertebrate retina is a thin layer of neural tissue lining the back of the eye that samples visual information from the environment before it reaches the visual centers of the brain. Photoreceptor cells are responsible for absorbing light energy or photons and transforming these into electrical signals that pass through a series of interneurons (bipolar, amacrine, and horizontal cells) before reaching the retinal ganglion cells (RGCs), whose axons form the optic nerve. The optic nerve is organized so that retinotopic information processed at the level of the retina is carried to specific regions of the central nervous system (McIlwain, 1996). The density of photoreceptors and RGCs is not homogeneous across the retina (Bozzano & Collin, 2000; Hughes, 1977; Schiviz, Ruf, Kuebber-Heiss, Schubert, & Ahnelt, 2008; Wagner, Frohlich, Negishi, & Collin, 1998; Walls, 1942). Regions of the retina with a higher density of photoreceptors and RGCs are known as retinal specializations (Meyer, 1977; Walls, 1942). These specializations provide higher spatial resolving power in discrete regions of the visual field (Collin, 1999). Therefore, animals rely on these specializations to obtain high quality information about their environment.

Across vertebrates, different types of retinal specializations have been identified, such as foveae, areae, and visual streaks, each varying in number, size, shape, and position in the retina (Collin, 1999; Collin & Shand, 2003; Hughes, 1977; Walls, 1942). A fovea is a pitted invagination of retinal tissue with a high density of photoreceptors and is surrounded by high densities of RGCs, where the inner retinal layers are displaced and the elongated photoreceptors attain their highest level of cell packing. The fovea is considered to mediate the highest spatial resolving power of all retinal specializations (Inzunza, Bravo, & Smith, 1989; Ross, 2004). An area is a concentric increase in ganglion cell or photoreceptor density, but without any obvious retinal displacement of the retinal layers. A visual streak is a band-like area extending horizontally across the retina allowing higher spatial sampling of a panoramic visual field. Each species possesses a specific arrangement of retinal specializations, which appears to be under selective pressure by virtue of its ecological niche, ambient light conditions, and habitat complexity (Collin, 1999).

Studying the distribution of neurons across the retina, or retinal topography, of a given species can help us understand how organisms visually perceive their environment, which ultimately affects their behavior (Fernández-Juricic, Gall, et al., 2011; Temple, Hart, Marshall, & Collin, 2010). For instance, among falconiform birds, predatory species have been shown to possess both central and temporal foveae, whereas the carrion-eating species have a single central fovea (Inzunza, Bravo, Smith, & Angel, 1991). Differences in the location of the retinal specializations in these species may be related to foraging strategies: predatory species are involved in more visually demanding tasks than carrion-eating species, which could account for the presence of the second foveae (Inzunza et al., 1991).

The comparative assessment of the diversity in retinal topography has important implications for better understanding the adaptations of the vertebrate visual system to different environmental conditions. This is particularly relevant given the large number of species whose retinal topography has been examined. Collin (2008) collated published topographic maps and released a public archive (see http://www.retinalmaps.com.au/) with over 300 species of vertebrates and over 1,000 maps. Despite some studies characterizing cell density gradients across the retina (Wässle & Boycott, 1991; Wässle, Grünert, Röhrenbeck, & Boycott, 1989), at present there is no single standard method for measuring retinal specialization traits quantitatively, such as type, position, and changes in cell density from the retinal periphery to the center of different retinal specializations. Such a capability would harness the power of this large comparative resource and allow us to test more challenging hypotheses regarding the evolution of vision across vertebrate taxa.

The aim of this study is to present a novel method to quantify the position of the retinal specialization and the concomitant changes in cell density across the retina. Additionally, using a commonly used statistical tool (discriminant function analysis [DFA]), we determined whether traits obtained by our method (retinal specialization position and cell density gradients) in combination with other retinal traits (peak and lowest ganglion cell densities) would be sensitive enough to distinguish among three common types of retinal specializations (fovea, area, or visual streak) in terrestrial and aquatic vertebrates. The methodological procedures presented in this study will have wide applicability in a comparative context by allowing us to standardize the measurement of retinal features from already published topographic maps in species with different eye size, orbit position in the skull, and overall retinal cell density.

Methods

This section is divided in three main parts. First, we describe the database on topographic maps gathered for this study. Second, we explain in detail the novel method we used to collect information on retinal specialization position, ganglion cell density gradients, and peak and lowest cell densities from topographic maps. Finally, we test our method by incorporating these retinal parameters into a DFA to test whether they can classify the topographic maps correctly into different types of retinal specializations (fovea, area, or visual streak).

Topographic maps database

We used published topographic maps of the RGC layer instead of the photoreceptor layer because they are more readily available in the literature. The original data consisted of counts of RGCs in different regions of the retina that were used to build the topographic maps. Most of the maps used in this study are available in the retinal topographic map database: http://www.retinalmaps.com.au/ (Collin, 2008). We used topographic maps from 88 species of vertebrates (Chondrichthyes, 6; Actinopterygii, 25; Amphibia, 1; “Reptilia,” 2; Aves, 21; Mammalia, 33; Appendix 1). Within Mammalia, we did not use the published topographic maps of the human retina (Curcio & Allen, 1990; Harman, Abrahams, Moore, & Hoskins, 2000), as they were not technically compatible with our methods. In the text, we used the common names of the species, but scientific names are available in Appendix 1. We classified species as aquatic if part of their life cycle relied on water for foraging and/or breeding purposes. Otherwise, species were considered terrestrial (Appendix 1).

We chose topographic maps that provided the orientation and scale of the retina with easily distinguished and properly labeled iso-density lines. We classified retinal specializations into three categories (fovea, area, and visual streak) based on the descriptions and topographic maps presented in the original published papers and some specific criteria (details in Appendix 2). In a limited number of studies, more than one map per species was available, and we chose the one the authors deemed most representative. The topographic map of each species was taken as the unit upon which we made measurements on different retinal traits (see below).

From the topographic maps (see example in Figure 1a), we quantified eight traits: (1–2) position of the retinal specialization with two coordinates, (3–6) changes in ganglion cell density from the retinal periphery to the center of the retinal specialization (cell density gradient) in four different regions of the retina (nasal, temporal, dorsal, and ventral), (7) peak RGC density, and (8) lowest RGC density. The position of the retinal specialization is relevant to establish the projection of the area with the highest spatial resolving power into the visual field (Collin, 1999). For instance, in a species with laterally-placed eyes, a temporal retinal specialization will project into the binocular visual field. The ganglion cell density gradient from the retinal periphery to the center of the retinal specialization varies substantially between species (Dolan & Fernández-Juricic, 2010). This cell density gradient is a proxy for how improved spatial resolving power provided by the retinal specialization is compared to the retinal periphery (Fernández-Juricic, Moore, et al., 2011). For instance, species with a steep cell density gradient are expected to rely more on the retinal specialization for visualizing objects, which could in turn affect patterns of visual search and visual fixation (Fernández-Juricic, Moore, et al., 2011). Finally, the highest and lowest RGC densities are proxies for the maximum and minimum levels, respectively, of spatial resolving power within the retina. The peak RGC density has been used in the calculation of the upper levels of visual acuity in some species (Boire, Dufour, Theoret, & Ptito, 2001; Collin & Pettigrew, 1989; Dolan & Fernández-Juricic, 2010; Hughes, 1977; Pettigrew et al., 1988).

(a) Topographic map of the retinal ganglion cell distribution of the California Towhee Pipilo crissalis (Fernández-Juricic, Gall, et al., 2011). Shown are iso-density lines (connecting areas of the retina with the same cell density). (b) Circle fitting of the edges of the retina. (c) Angle between the center of the retinal specialization and the nasal axis of the retina. The gray dot represents the center of the retina and the black dot, the center of the retinal specialization. (d) Distance from the center of the retina to the center of the retinal specialization (2.62). This distance is divided by the radius of the circle (10.65) to obtain a standardized distance of the retinal specialization to the center of the retina (0.25).

Figure 1

(a) Topographic map of the retinal ganglion cell distribution of the California Towhee Pipilo crissalis (Fernández-Juricic, Gall, et al., 2011). Shown are iso-density lines (connecting areas of the retina with the same cell density). (b) Circle fitting of the edges of the retina. (c) Angle between the center of the retinal specialization and the nasal axis of the retina. The gray dot represents the center of the retina and the black dot, the center of the retinal specialization. (d) Distance from the center of the retina to the center of the retinal specialization (2.62). This distance is divided by the radius of the circle (10.65) to obtain a standardized distance of the retinal specialization to the center of the retina (0.25).

We first established the location of the center of the retinal specialization in the topographic map. For a fovea, given its relatively small size, the position was generally marked in the topographic map as a point. The fovea can be identified from a wholemounted retina as a circular pit on the retinal tissue. However, the area and the visual streak occupy a relatively larger spatial extent than the fovea (Walls, 1937). Therefore, we determined the center of either type of retinal specialization as the point with the highest cell density identified in each published topographic map. If this point was not reported, we marked it as the middle point within the highest cell density range because the highest cell density is usually located at the center of the upper cell density range in most topographic maps (Collin, 2008).

To quantify the position of the retinal specialization, we used a Cartesian coordinate system (see also Mastronade, Thibeault, & Dubin, 1984). Because the outer edges of the retina are removed in a nonuniform fashion during the retinal wholemounting process (Stone, 1981; Ullmann, Moore, Temple, Fernández-Juricic, & Collin, 2012; Figure 1a), we fitted a circle over the retina by eye based on two criteria: the circle encompassed as much of the retina as possible, and the gaps between the circle and the periphery of the retina were minimized (Figure 1b). Once the circle was fitted over the retina, we determined the center of the circle as the intersection of any two diameters, which were traced with Autocad 2010 (Autodesk, San Rafael, CA, USA, http://usa.autodesk.com/autocad/).

From the center of the retina, we then measured the angle of the retinal specialization (in degrees, Θ). The nasal part of the retina was considered as 0° for both right and left eyes, which allowed us to standardize measurements across species irrespective of the eye used to generate the topographic map. We then established 90° as dorsal, 180° as temporal, and 270° as ventral (Figure 1b). The angle of the retinal specialization was measured in relation to the nasal direction (Figure 1c). We measured the relative distance from the center of the retina to the center of the retinal specialization. We first drew a line from the center point of the retina to the retinal specialization (Figure 1d) and measured this distance with the aligned measurement tool in Autocad 2010 (Figure 1d). We divided this distance by the radius of the circle to obtain a standardized distance (Figure 1d), which varied from 0 to 1.

We converted the angle of the retinal specialization (Θ) and its distance to the center of the retina (r) into Cartesian coordinates, which are both linear (x and y) and can be any positive or negative number (Figure 2). We used (r)cosΘ to obtain the x-coordinate and (r)sinΘ to obtain the y-coordinate. Cartesian coordinates consist of two linear positive and/or negative values; thus, a right and left retina will provide different x-coordinate values since the eye is flipped around the y-axis. To maintain consistency, we made right eyes the standard, inversing the sign of the x-coordinate for left eyes. Using Cartesian coordinates assumes that the wholemounting process was done similarly across studies to produce the topographic maps. However, this is unlikely to be the case, which could introduce a certain degree of error in our measurements (see more details in the Discussion).

Cartesian coordinates to establish the position of the retinal specialization in the retina. The coordinates consist of two linear distances (x- and y-coordinates) of both positive and negative values, depending on whether the position of the specialization is on the dorsal, ventral, nasal, or temporal sides of the retina.

Figure 2

Cartesian coordinates to establish the position of the retinal specialization in the retina. The coordinates consist of two linear distances (x- and y-coordinates) of both positive and negative values, depending on whether the position of the specialization is on the dorsal, ventral, nasal, or temporal sides of the retina.

(a) Example of the cell density points at the intersection of the iso-density lines along the nasal-temporal and dorsal-ventral vectors crossing the center of the retinal specialization. Notice that the line extends into the radial cuts of the retina (see text for details). (b) Example of the 21 cell density sampling points along the nasal-temporal vector, which divided the sampling line into 20 even spaces. At each point, we measured the mean cell density value that it fell in. (c) Example of the plot of the mean cell density in each sampling point from the temporal periphery of the retina to the center of the retinal specialization. We fitted a line and used its slope as the rate of change in cell density from the retinal periphery to the retinal specialization.

Figure 3

(a) Example of the cell density points at the intersection of the iso-density lines along the nasal-temporal and dorsal-ventral vectors crossing the center of the retinal specialization. Notice that the line extends into the radial cuts of the retina (see text for details). (b) Example of the 21 cell density sampling points along the nasal-temporal vector, which divided the sampling line into 20 even spaces. At each point, we measured the mean cell density value that it fell in. (c) Example of the plot of the mean cell density in each sampling point from the temporal periphery of the retina to the center of the retinal specialization. We fitted a line and used its slope as the rate of change in cell density from the retinal periphery to the retinal specialization.

We set sampling points along two pairs of vectors (nasal-temporal and dorsal-ventral; Figure 3a and b). Along each pair of vectors, we established 21 evenly-spaced sampling points (Figure 3b shows an example with the nasal-temporal vector), with the first and last sampling point marking the edges of the retina, yielding 20 evenly-spaced intervals (Figures 3b and 4d). At each of the 21 sampling points, the average density of RGCs was recorded by determining which iso-density lines each sampling point fell into (i.e., between which iso-density lines; Figure 4a through f).

Example of how to determine the mean cell density for each of the 21 sampling points. Shown are the first 13 and the last sampling points for the sake of clarity. Distances were scaled to mm to fit the scale provided in the topographic maps. Open circles represent the iso-density lines, and solid circles are the evenly spaced sampling points. The mean RGC density is an average of the RGC range between two iso-density lines. The edges of the retina are marked with sampling point 1 (0.00 mm) and 21 (12.28 mm). Sampling point 13 is the point that falls along the vector prior to crossing over the peak cell density of the retinal specialization. See explanation of the different steps (a through f) in the text.

Figure 4

Example of how to determine the mean cell density for each of the 21 sampling points. Shown are the first 13 and the last sampling points for the sake of clarity. Distances were scaled to mm to fit the scale provided in the topographic maps. Open circles represent the iso-density lines, and solid circles are the evenly spaced sampling points. The mean RGC density is an average of the RGC range between two iso-density lines. The edges of the retina are marked with sampling point 1 (0.00 mm) and 21 (12.28 mm). Sampling point 13 is the point that falls along the vector prior to crossing over the peak cell density of the retinal specialization. See explanation of the different steps (a through f) in the text.

First, we measured the distance (mm) between iso-density lines along a given vector (nasal-temporal and dorsal-ventral; Figure 4b). Second, we measured the cumulative distance (mm) at each iso-density line (Figure 4c). Third, we determined the distance (mm) between each sampling point along the vector by multiplying the total length of the vector (e.g., 12.28 mm in Figure 4) by 0.05 (e.g., 0.614 mm in Figure 4) to establish 21 sampling points that were equidistant to each other (Figure 4d). Fourth, we calculated the cumulative distances across sampling points along a given vector (Figure 4e). Fifth, if the cumulative distance up to a particular sampling point was smaller than the cumulative distance up to the iso-density line with the next higher cell density value, we established the mean RGC density for that particular sampling point to be the averaged density between the upper and lower cell density ranges bounded by the iso-density lines that the sampling point fell into (Figure 4f). For instance, in Figure 4, the cumulative distance up to sampling point 3 is 1.228 mm (Figure 4e), which is smaller than the cumulative distance up to the proceeding iso-density line 4, 1.841 mm, with a higher cell density value (Figure 4e). Therefore, the final cell density value obtained for sampling plot 3 was estimated to be 7,500 cells/mm2 (i.e., average of the cell density range 5,000–9,900 cells/mm2; Figure 4f). We followed the same procedure to estimate the cell densities of all other sampling points, which were used for the calculation of the slope.

The number of sampling points (21) along a given vector allowed us to capture the high diversity in iso-density line configurations present in the published topographic maps used in this study. We tried using fewer sampling points, but missed changes in iso-density categories in some of the topographic maps. In some cases, some of the 21 sampling points did not fall within the peak density range of the retinal specialization. To determine whether or not this caused a significant change in our slope estimates, we increased the number of sampling points to include the cell density range of the retinal specialization and recalculated the slope. We found that these two measurements were highly correlated (nasal, r = 0.99, p < 0.001; temporal, r = 0.96, p < 0.001; dorsal, r = 0.99, p < 0.001; ventral, r = 0.99, p < 0.001). Consequently, we decided to use the 21 sampling points to be consistent across all topographic maps.

In some cases, the published topographic maps did not include the RGC density for the outer perimeter of the retina. For these maps, when a sampling point fell into the peripheral cell density range, we established that the cell density would be half of the density of the first iso-density line shown nearest the periphery, based on patterns observed in maps that included this piece of information. For instance, if the first peripheral iso-density value was 500 cells/mm2, a sampling point falling into this range would have a ganglion cell density value of 250 cells/mm2. After the RGC density values had been recorded for all 21 points on the pairs of vectors (nasal-temporal and dorsal-ventral), we split them into four separate vectors (nasal, temporal, ventral, and dorsal). We then plotted the mean RGC density values at each sampling point and fitted the changes in cell density across the retina with a linear and nonlinear functions (second order polynomial). From the linear fitting, we used the slope of that line as a proxy for the gradient in cell density change from the retinal periphery to the retinal specialization (example in Figure 3c). From the nonlinear fitting, we used the coefficients of the first and second order polynomials as the proxies for the gradient in cell density change. We also ran the analyses with a third order polynomial (data not shown; results available from the corresponding author), but the fit was even worse than the linear and second order polynomial. We took this dual approach (linear and nonlinear) in the cell density gradient characterization since some of the gradients deviated from linearity.

For instance, in some topographic maps (pigmented rabbit, black bream, painted flutemouth, spookfish, and staghorn damselfish), we could only get two different cell density values on a specific retinal direction (e.g., a plateau followed by a sudden increase in cell density) because of the low number of iso-density categories or because the retinal specialization was too close to the edge of the retina, reducing the number of sampling points on that specific direction of the retina. For the linear approach, we fitted the data with a Multivariate Adaptive Regression Splines (MARSplines) analysis, which yielded a weighted slope based on slopes from lines fitted to different parts of the relationship based on differences in the coefficient of determination (Statsoft, 2012). The slope values obtained from the MARSplines analysis were similar to those obtained through linear regression fitting. Therefore, we decided to use the latter so that the slope values were comparable across species. Using a similar procedure for all taxa is particularly important for the application of our method in comparative analyses. Finally, the gradient in cell density change in the nasal regions of the great kiskadee, coral cod, carangid fish, small dogfish, and softskin smoothhead showed a pattern of increasing-decreasing-increasing cell density from the retinal periphery to the center of the retinal specialization. To determine if the slopes of cell density change on a single retinal direction of these species would bias the conclusions of the linear approach, we reran our statistical analysis classifying retinal specializations based on the studied traits (DFA, see below) excluding these species, but the overall classification scores were very similar to the analysis including these species (available from the corresponding author upon request). We therefore included these five species in the analyses to assess the discrimination ability of the model based on a wide range of retinal topographic configurations.

Peak and lowest cell density

From the original publications and the topographic maps, we obtained the peak RGC density. The lowest cell density was obtained from the topographic maps as the cell density at the periphery of the retina. In some cases, the cell density at the periphery was not available. We then established the cell density as half of the density of the first iso-density line reported in the topographic map (see below).

Statistical analysis

The analysis included measurements from 26 foveae, 35 visual streaks, and 33 areae. Six species were represented twice in our dataset (Appendix 1) due to the presence of two retinal specializations in different regions of their retinas: Chilean eagle and American kestrel (central and temporal foveae), and rock pigeon, great kiskadee, and rusty-marginated flycatcher (central fovea and area temporalis), and harlequin tuskfish (streak and area). We decided to include the second retinal specialization from each of these species due to the different morphologies within each retina (e.g., the central retinal specialization had a higher cell density than the temporal) and to determine if our method could tell the two types of specializations apart on a given species. However, we acknowledge that this introduced a bias by having two data points from each of these six species. We justified this on the basis that this study focuses on presenting a novel method rather than analyzing retinal configurations from a comparative perspective controlling for the effects of phylogenetic relatedness.

We used a DFA (Huberty, 1994; Quinn & Keough, 2002) to assess the ability of our method to assign the different topographic maps to three types of retinal specializations (fovea, area, and visual streak). We chose the DFA over other classification techniques (e.g., artificial neural networks) because its results are easier to interpret. We included in the DFA the eight retinal traits studied for each topographic map, along with the type of retinal specialization. The DFA generated canonical discriminant functions based on the linear combinations of the eight retinal traits maximizing the probability of correctly assigning cases (e.g., topographic maps) to specific categories (e.g., type of retinal specialization; Huberty, 1994). The DFA used the relative sizes of the standardized coefficients of each discriminant function (Huberty, 1994) to establish the retinal traits that best discriminated among types of retinal specializations. By solving the discriminant functions, the DFA estimated discriminant function scores for each topographic map on each function (Quinn & Keough, 2002). This information was used in a canonical correlation analysis to plot the values of each topographic map along the roots (i.e., eigenvalues associated with the respective discriminant function; Statsoft, 2012) to assess visually the degree to which observations belonging to different types of retinal specializations grouped together (e.g., Figures 5 and 6 show the roots of the canonical analysis). Additionally, the DFA derived a classification equation for each type of retinal specialization (Quinn & Keough, 2002), which was used to estimate a classification score for each topographic map. Then each topographic map was assigned to the type of retinal specialization based on its classification score, which allowed the DFA to estimate the percentage of observations that were correctly classified (Quinn & Keough, 2002). The DFA shares assumptions with general linear models (Tabachnick & Fidell, 1996).

Scatterplot of the discriminant functions (canonical axis scores) showing the discrimination of the three types of retinal specializations (fovea, area, and visual streak) for terrestrial vertebrates. We used two approaches, (a) linear and (b) nonlinear, to quantify cell density gradients (details in the text). Only two canonical axis scores were computed in each case. RS, retinal specialization.

Figure 5

Scatterplot of the discriminant functions (canonical axis scores) showing the discrimination of the three types of retinal specializations (fovea, area, and visual streak) for terrestrial vertebrates. We used two approaches, (a) linear and (b) nonlinear, to quantify cell density gradients (details in the text). Only two canonical axis scores were computed in each case. RS, retinal specialization.

Scatterplot of the discriminant functions (canonical axis scores) showing the discrimination of the three types of retinal specializations (fovea, area, and visual streak) for aquatic vertebrates. We used two approaches, (a) linear and (b) nonlinear, to quantify cell density gradients (details in the text). Only two canonical axis scores were computed in each case. RS, retinal specialization.

Figure 6

Scatterplot of the discriminant functions (canonical axis scores) showing the discrimination of the three types of retinal specializations (fovea, area, and visual streak) for aquatic vertebrates. We used two approaches, (a) linear and (b) nonlinear, to quantify cell density gradients (details in the text). Only two canonical axis scores were computed in each case. RS, retinal specialization.

For the DFA, we used Wilks' Lambda as the test statistic, which was then used to estimate an F statistic and p-value. Given that some of the traits we measured had a high degree of correlation (>0.70; peak RGC density and nasal, dorsal, and ventral gradient in cell density), we used a forward stepwise selection method to enter the traits in the model. This model selection procedure enhanced the classification score of the DFA in comparison to standard selection procedures forcing all traits into the model. In the DFA, we used a-priori classification probabilities that were proportional to group sizes (Statsoft, 2012). We first ran the DFA model, pooling terrestrial and aquatic species together, and then considered them separately due to potential differences in retinal configuration (Mass & Supin, 2007). We ran two sets of DFA models, one for the linear and one for the nonlinear approach. For the DFA using the linear approach, we included the following parameters: peak RGC density, lowest RGC density, x-coordinate position, y-coordinate position, and nasal, temporal, dorsal, and ventral slopes. For the DFA using the nonlinear approach, we had two slope coefficients (first and second order polynomials) in each of the four retinal directions. Because these coefficients are not independent of each other, we ran a principal component analysis (PCA) to combine the two coefficients into a single factor before running the DFA models. Thus, for the DFA using the nonlinear approach, we included the following parameters: peak RGC density, lowest RGC density, x-coordinate position, y-coordinate position, nasal PCA factor, temporal PCA factor, dorsal PCA factor, and ventral PCA factor. Therefore, the DFA models using the linear and nonlinear approaches included the same number of parameters.

Results

We obtained measurements on all the retinal traits from 94 topographic maps belonging to 88 species of vertebrates (Table 1). Based on the coefficients of variation, position in the x- and y-coordinates showed the highest degree of variability between species, whereas peak RGC density and nasal gradient in cell density showed the lowest (Table 1). Different taxa were represented in the extreme values of the traits measured. The minimum values of the lowest and highest RGC density and cell density gradient in all regions of the retina were represented by mammals, and the minimum values of the x- and y-coordinate were represented by cartilaginous and ray-finned fishes (Actinopterygii and Chondrichthyes; Table 1). The maximum values of lowest and peak RGC density gradients and nasal, temporal, and ventral gradients in cell density were represented by birds, whereas the maximum values of the dorsal gradient in cell density and x- and y-coordinates were represented by ray-finned fish (Actinopterygii; Table 1).

Considering all species, the DFA with a linear approach selected five factors out of the eight: nasal and dorsal gradients in cell density, lowest RGC density, and x- and y-coordinate positions of the retinal specialization. With these factors, the DFA significantly discriminated among the three retinal specializations, F(10, 174) = 6.37, p < 0.001. This DFA correctly classified 66% of the retinal specializations to the correct type. The visual streak (28 out of 35, 80%) and the fovea (16 out of 26, 61.5%) had the highest classification scores, whereas the area (18 out of 33, 54.6%) had the lowest. The DFA with a nonlinear approach selected six factors that yielded a significant discrimination among retinal specializations, F(12, 172) = 5.24, p < 0.001: nasal, dorsal, and ventral PCA factors representing the gradients in cell density, lowest RGC density, and x- and y-coordinate positions of the retinal specialization. The DFA with a nonlinear approach correctly classified 67% of the retinal specializations to the correct type. The visual streak (30 out of 35, 85.7%) had the highest classification scores, followed by the fovea (15 out of 26, 57.7%) and the area (18 out of 33, 54.6%). Models with both approaches (linear and nonlinear) performed at similar levels.

We found that sorting species out into terrestrial versus aquatic increased the overall classification scores of the DFA models. Considering terrestrial species, five factors were selected by the DFA with a linear approach to discriminate significantly among the retinal specializations, F(10, 104) = 11.18, p < 0.001: peak and lowest RGC densities, temporal gradient in cell density, x- and y-coordinate positions of the retinal specialization. This DFA model increased the overall classification score of the 59 topographic maps of terrestrial species to 77.97%. The visual streak (23 out of 24, 95.8%) and the fovea (20 out of 22, 90.9%) had the highest classification scores, whereas the area (3 out of 13, 23.1%), the lowest. In nine mammal species, the area was misclassified as a visual streak (Table 2). The DFA with a nonlinear approach for terrestrial species also discriminated significantly among retinal specializations, F(12, 102) = 9.11, p < 0.001, including six factors: peak and lowest RGC densities, x- and y-coordinate positions of the retinal specialization, and dorsal and temporal PCA factors representing the gradients in cell density. The overall classification score of this DFA was 79.7%, with the visual streak (23 out of 24, 95.8%) and the fovea (20 out of 22, 90.9%) having the highest scores, and the area the lowest (4 out of 13, 30.77%). In eight mammal species, the visual streak was misclassified (Table 2). Models with both approaches (linear and nonlinear) for terrestrial species performed at similar levels.

Topographic maps of terrestrial vertebrates that were misclassified by the DFAs considering different retinal traits (see text for details). Two approaches were used (linear and nonlinear) for the classification. Scientific names are presented in Appendix 1. RS, retinal specialization.

Table 2

Topographic maps of terrestrial vertebrates that were misclassified by the DFAs considering different retinal traits (see text for details). Two approaches were used (linear and nonlinear) for the classification. Scientific names are presented in Appendix 1. RS, retinal specialization.

Species common name

Type of RS

Misclassified using the linear approach as

Misclassified using the nonlinear approach as

Peafowl

area

fovea

fovea

Mouse lemur

area

visual streak

visual streak

Tree kangaroo

area

visual streak

visual streak

North American opossum

area

visual streak

visual streak

Three-toed sloth

area

visual streak

N/A

Golden hamster

area

visual streak

visual streak

Ferret

area

visual streak

visual streak

Galago

area

visual streak

visual streak

Koala

area

visual streak

visual streak

Hooded rat

area

visual streak

visual streak

Anubis baboon

fovea

visual streak

area

Owl monkey

fovea

visual streak

visual streak

Beagle

visual streak

area

area

The plots of the first and second canonical axis scores (roots 1 and 2 in Figure 5) of the terrestrial species for both the linear and nonlinear approaches for quantifying cell density gradients show that there is little overlap between the fovea and the visual streak (Figure 5a and b), which were discriminated mostly along the first canonical axis scores (root 1). Based on the factors with the higher loadings on the canonical axes, species with a fovea showed higher peak and lowest RGC density, whereas species with a visual streak showed a shallower temporal gradient in cell density. The area had intermediate values along root 1 (Figure 5a and b). With respect to the second canonical axis scores (root 2 in Figure 5), a slightly larger number of species with foveae and visual streaks had their retinal specialization located in the dorsal and temporal areas of the retina (Figure 5a and b). The main difference between the linear and nonlinear approaches was the bottom-left corner of the plot of the canonical axis scores. In the linear approach, this sector corresponded to species exhibiting shallow temporal gradients in cell density between the retinal periphery and the retinal specialization (Figure 5a), whereas in the nonlinear approach, this sector corresponded to species with more nasal and ventral retinal specializations (Figure 5b). Overall, the area overlapped more with the visual streak than with the fovea (Figure 5).

When considering only the aquatic species, seven factors were selected by the DFA with the linear approach for quantifying cell density gradients to discriminate significantly among the retinal specializations, F(14, 52) = 3.06, p = 0.002: x- and y-coordinate positions of the retinal specialization, peak and lowest RGC densities, and temporal, nasal, and dorsal gradients in cell density. This DFA model assigned 85.7% of the topographic maps to the correct type of retinal specialization (Appendix 2). The area had the highest classification scores (18 out of 20, 9%), whereas the visual streak (9 out of 11, 81.8%) and the fovea (3 out of 4, 75%) had the lowest classification scores. In this DFA model, the most common misclassifications were visual streaks that were sorted as areae in two fish species (Table 3). The DFA model with the nonlinear approach discriminated significantly among the three retinal specializations, F(12, 54) = 9.11, p < 0.001. This model included six factors: peak and lowest RGC densities, x- and y-coordinate positions of the retinal specialization, and dorsal and temporal PCA factors representing the gradients in cell density from the retinal periphery to the retinal specialization. The model classified correctly 77.1% of the cases. The area had the highest classification score (17 out of 20, 85%), followed by the visual streak (8 out of 11, 72.7%) and the fovea (2 out of 4, 50%). The visual streak and the area were commonly misclassified in five fish species (Table 3). The DFA model with a linear approach for aquatic vertebrates performed better than the model with the nonlinear approach.

Topographic maps of aquatic vertebrates that were misclassified by the DFAs considering different retinal traits (see text for details). Two approaches were used (linear and nonlinear) for the classification. Scientific names are presented in Appendix 1. RS, retinal specialization.

Table 3

Topographic maps of aquatic vertebrates that were misclassified by the DFAs considering different retinal traits (see text for details). Two approaches were used (linear and nonlinear) for the classification. Scientific names are presented in Appendix 1. RS, retinal specialization.

Species common name

Type of RS

Misclassified using the linear approach as

Misclassified using the nonlinear approach as

Florida garfish

visual streak

area

area

Lemon shark

visual streak

area

area

Harp seal

area

visual streak

visual streak

Coral cod

area

fovea

N/A

Searsid

fovea

area

N/A

Bigfin pearleye

area

N/A

visual streak

Creek chub

area

N/A

visual streak

Harlequin tuskfish

visual streak

N/A

area

Legless searsid

fovea

N/A

area

Searsid

fovea

N/A

visual streak

The plot of the first and second canonical axis scores (roots 1 and 2 in Figure 6) of the aquatic species shows a clear segregation among the fovea, area, and visual streak in the linear and nonlinear approaches (Figure 6), particularly along the first canonical axis (root 1 in Figure 6). Based on the factors with the higher loadings on the canonical axes, foveae had higher peak and minimum RGC densities and steeper temporal slopes. Visual streaks had shallower temporal gradients in cell density, higher peak RGC densities, and the fovea was placed more nasally and temporally. Finally, areae showed intermediate values between these extremes (Figure 6a and b). The factors associated with the canonical axes were different between the models with the linear and nonlinear approaches (Figure 6).

Both DFA model approaches yielded classification functions for each type of retinal specialization considering terrestrial and aquatic species (Appendix 3). These functions can be used in the future for the calculation of classification scores for species not used in this analysis to further test the classification ability of the models.

Discussion

We presented a novel method to characterize retinal traits based on topographic maps of the RGC layer. This method estimates the position of the retinal specialization and the gradient in cell density from the retinal periphery towards the retinal specialization in four axes relevant to the visual ecology of the animal. This information was complemented with the peak and lowest ganglion cell densities available from the topographic maps. Our method provides a quantitative way of evaluating changes in retinal specialization traits across species to test in the future different visual ecology hypotheses. We found that our method is sensitive to identifying common types of retinal specializations in terrestrial and aquatic mammals (fovea, area, and visual streak), which have been generally distinguished on the basis of size and cross-sections of the area with the highest cell density in the retina (Collin, 1999; Hughes, 1977; Walls, 1942). Furthermore, our method can be used to identify retinal topographies that would support different types of retinal specializations on the same retina.

Traditionally, the position of a retinal specialization has been characterized in discrete categories, such as dorsal, ventro-nasal, central, etc. (Hughes, 1977; Meyer, 1977; Walls, 1942). However, this categorization prevents us from making quantitative estimations that can be used to compare the position of the retinal specialization across species living in different visual environments. Quantitative estimates can allow us to determine more accurately the specific position in the visual field that the retinal specialization projects to, which has important behavioral implications (e.g., foraging, Collin, 1999; anti-predator behavior, Fernández-Juricic, 2012; predator-prey interactions, Cronin, 2005). Our method estimates the position of retinal specializations using a Cartesian system that takes into consideration the angle of the retinal specialization in relation to the nasal direction, as well as the distance between the retinal specialization and the center of the retina. For instance, we found that in terrestrial vertebrates, the fovea and visual streak are located more dorsally and temporally, whereas in aquatic vertebrates, the fovea appears to be more ventrally placed. These trends can be tested in future studies using comparative methods controlling for phylogenetic effects.

Our index of the steepness of the gradient in cell density can offer insight into the degree of spatial resolving power provided by the retinal specialization in relation to that of the retinal periphery (Dolan & Fernández-Juricic, 2010; Whiteside, 1967). We found a trend that suggests that foveae have steeper gradients (and thus a more pronounced change in spatial resolving power) from the retinal specialization to the retinal periphery and higher peak ganglion cell density in relation to areae and visual streaks. Future comparative studies should assess whether animals with a steep decline in visual resolution towards the retinal periphery rely more heavily upon the retinal specialization for visualizing objects (Fernández-Juricic, Gall, et al. 2011).

We used linear and nonlinear approaches for classifying different retinal specializations, which overall performed similarly. However, both approaches were less successful in discriminating among the three retinal specializations when we combined terrestrial and aquatic species than when we considered these groups separately. This could be related to variations in the retinal configuration beyond the known differences in eye characteristics between terrestrial and aquatic vertebrates (Dral, 1972; Mass & Supin, 2007). Compared to terrestrial species, aquatic species appear to have higher densities and larger RGCs (Mass & Supin, 2010), higher densities of amacrine and neuroglial cells (Mass & Supin, 2000), lower numbers of cone photoreceptors (Peichl, Berhmann, & Kroger, 2001), and a higher maximum number of retinal specializations per retina (Collin, 1999). Many of these differences are also taxa-specific (Collin, 1999). The implication is that future comparative studies on retinal topography should assess terrestrial and aquatic species separately.

In terrestrial species, the DFA provided good discrimination (above 90%) for foveae and visual streaks, but lower discrimination for areae. On the contrary, in aquatic species, the linear DFA in particular discriminated areae better than foveae and visual streaks. One potential factor is that the retinal specialization type with the lower discrimination in either model was the one with the lowest sample size. Additionally, in terrestrial species, areae were generally misclassified as visual streaks, whereas in aquatic species, visual streaks were generally misclassified as areae. In three of the terrestrial mammals with a misclassified area (golden hamster, ferret, and hooded rat), the topographic maps showed an area where the lower cell density isolines were slightly elongated, which is sometimes referred to in the literature as a “weak” visual streak (Collin & Pettigrew, 1988a, b), although it does not meet the morphological criteria we used for visual streaks (Appendix 2). Finally, some of the authors' original classifications included two types of retinal specializations overlapping (e.g., area and visual streak). We chose one based on specific criteria (Appendix 2) for the DFA. However, the lower classification success of some topographic maps suggests that some observed retinal specializations may be intermediate between two different types. Our method has the potential to quantify this degree of variability.

One trait that could facilitate the discrimination of an area from a visual streak in the future is the spatial extent of these retinal specializations. It is assumed that areae are smaller than visual streaks (Collin, 1999; Hughes, 1977). Although the spatial limits of foveae are easier to distinguish morphologically from the whole-mounted retina (e.g., the width of the foveal pit), the same does not apply to areae and visual streaks. For instance, the area is defined as a thickening of the retinal tissue; however, there is no established criterion to determine where the thickening begins in a cross-section, let alone in a topographic map. The same is true for the visual streak, as the density thresholds that bound the band of high cell density (hence, spatial resolving power) across the retina are yet to be established. Our method actually identified species that can be used to better understand the morphological differences between areae and visual streaks by comparing the aforementioned retinal traits in species that were correctly as well as incorrectly classified. Future work addressing the spatial limits of retinal specializations (e.g., expressed as the percentage of the peak RGC density) could improve the classification success of DFAs like the one used in this study.

Our method has some shortcomings. First, measuring the position of the center of the retinal specialization and the ganglion cell density gradient assumes that cell density increases from the periphery towards a single point of peak density in the retina. Consequently, our method is not applicable to the retinal specialization termed radial anisotropy, which is a concentric increase in ganglion cell density towards the periphery of the retina (Dunlop & Beazley, 1981). Determining the center of this retinal specialization is therefore not feasible using our method. Although the radial anisotropy has been reported in species such as the South African clawed frog Xenopus laevis (Dunlop & Beazley, 1984), the sawtoothed eel Serrivomer beani (Collin & Partridge, 1996), and Bonapart's spiny eel Notacanthus bonapartei (Wagner et al., 1998), it is not very common in vertebrates and is primarily reported in studies that have included amacrine cells within the ganglion cell layer, which may account for the higher cell density in the periphery. Second, our method is at the mercy of the publishing authors having oriented the wholemount correctly with regard to the nasal, dorsal, ventral, and temporal poles and the assumption that the shrinkage of the wholemount during processing was relatively similar in different species (Stone, 1981; Ullmann et al., 2012). Third, our method assumes that the cells counted are all RGCs, which in some cases are difficult to distinguish from other cell types (e.g., amacrine cells; Freeman & Tancred, 1978; Hayes & Holden, 1983; Hughes, 1977; Pettigrew, Dreher, Hopkins, McCall, & Brown, 1988).

Despite these limitations, we believe our novel method can be applied to characterize retinal morphology by standardizing the measurement of retinal traits (retinal specialization position, cell gradient, etc.) from published topographic maps in a wide range of vertebrate taxa. However, when working with taxa with a lower degree of variability in the studied retinal traits, the method can be slightly adjusted. For instance, there are some species with foveae (humans and primates) in which the RGC density increases gradually from the retinal periphery to the center of the retina, and then cell density sharply increases towards the fovea and eventually decreases to almost zero at the very center of the fovea. For these species, increasing the number of sampling points in the perifoveal and foveal areas may provide a better characterization of the gradients in cell density. In these cases, the nonlinear approach (even including third order polynomials) may fit the data better.

Although we did not test any specific hypothesis, the retinal traits measured can be used in combination with phylogenetic methods (Garland, Bennett, & Rezende, 2005; Harvey & Pagel, 1991; Nunn & Barton, 2001) to answer questions about the association between retinal morphology and behavioral, ecological, and life-history traits (Hall & Ross, 2007; Heesy, Kamilar, & Willms, 2011), which can shed light onto the evolution of the vertebrate visual system. Additionally, our method can be used to establish how different retinal specializations vary in position, ganglion cell density, and cell density gradients in taxa/species with different visual demands and that inhabit a diversity of ecological niches. Finally, the retinal traits measured can be used to distinguish between different types of retinal specializations using published topographic maps. This may be particularly important for rare, threatened, or endangered species, for example, where the availability of additional retinal material to use for further analysis (such as sectioning the retina in order to confirm the presence or absence of a fovea) is limited due to logistic or ethical considerations.

Acknowledgments

Partial funding for this project was provided to EFJ by the National Science Foundation (IOS-0641550/0937187) and Purdue University. The material presented in this study is based upon work supported by the National Science Foundation through the National Evolutionary Synthesis Center (NESCent) under grant number NSF #EF-0905606.

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In most of the retinal specializations (across 88 species, Appendix 1) included in this study, the authors' classification coincided with the general criteria to distinguish between retinal specializations. In general, we followed the authors' classification.

Of the three retinal specialization types we focused on in this study, the fovea is the only one that may be seen as a funnel-shaped mark on the wholemounted retina, although its presence should be confirmed through cross-sectional analysis showing tissue invagination. Many studies using topographic maps of the retinal ganglion cell (RGC) layer marked the presence of the fovea following visual inspection. The other retinal specializations studied (areae and visual streaks) are more difficult to classify based on the topographic representation of variations in the density of RGCs. Stone and Halasz (1989) emphasized that improving the classification of retinal specializations requires analyses beyond topographic maps; such as establishing the projections of the RGCs to centers in the brain.

Many of the topographic maps published already do not have further tests to confirm the type of retinal specializations. Nevertheless, by following some criteria from the literature (Collin, 2008; Hughes, 1977; Walls, 1937), we classified the three types of retinal specializations based on features detectable by examination of retinal topographic maps. In general terms, we considered the foveas an indentation of the retina showing a funnel-shaped pit in the retinal tissue (Collin, 2008; Walls, 1937). We considered the area as a round, localized concentration of ganglion cells without a noticeable pit in the retinal tissue (Hughes, 1977). Finally, we considered the visual streak as a “bandlike area” crossing along the retina (Hughes, 1977).

However, in some cases, the authors did not specify a type of retinal specialization or their classification did not follow necessarily the criteria presented above. We explain in the following paragraphs the criteria we used to classify these cases.

1.

Three-toed sloth (Costa, Pessoa, Bousfield, & Clarke, 1987; http://retinalmaps.com.au//view?tag0=157163). The authors classified this retinal specialization as both an area and a visual streak. However, we classified it as an area in our analysis. The first two iso-density lines are very circular (greater than 1,350 cells/mm2), with a concentric increase in RGC density up to a specific point, which follows the area definition (Hughes, 1977). The next two lower cell density isolines (bounding cell densities between 1,000–1,200 cells/mm2) have a tail that extends in the dorsal direction but not all the way to both sides of the retina. Furthermore, the lines representing even lower cell densities (beyond the fourth highest, less than 1,000 cells/mm2) do not remain elongated and are more circular.

2.

Ferret (Vilela et al., 2005; http://retinalmaps.com.au//view?tag0=157165). The retinal configuration is similar in principle to that of the three-toed sloth, in that the highest cell density ranges (greater than 4,500 cells/mm2) are circular like an area, then the next lower iso-denity line (between 3,500–4,500 cells/ mm2) becomes more elongated in one direction, but the lowest iso-density lines (less than 3,500 cells/mm2) become more circular. Therefore, we also classified this specialization as an area.

3.

The topographic maps of seven species of birds (California towhee and white-crowned sparrow, Fernández-Juricic, Gall, et al., 2011; European starling, brown-headed cowbird, house sparrow, house finch, and mourning dove, Dolan & Fernández-Juricic, 2010) were originally reported as having an area due to the lack of cross-sections. However, we confirmed through visual examination of their whole-mounted retinas that they have a funnel-shaped pit in the retinal tissue. Therefore, we classified them as all having foveae.

Also, each of the seven species (great kiskadee, rusty-marginated flycatcher, Chilean eagle, American kestrel, Chimango caracara, condor, and black vulture) was suggested in the original publications to also have a third retinal specialization: a visual streak. However, we did not assign these species as having a visual streak because the streak-like extension is only an effect of the two other specializations being close to one another rather than a distinctive bandlike area of high RGC density across the retina.

Additionally, two of the topographic maps included in the analysis (Carolina chickadee and white-breasted nuthatch) are currently in a manuscript in revision (Moore et al., 2012). These two species have a fovea that could be distinguished from the wholemount (see above).

(a) Topographic map of the retinal ganglion cell distribution of the California Towhee Pipilo crissalis (Fernández-Juricic, Gall, et al., 2011). Shown are iso-density lines (connecting areas of the retina with the same cell density). (b) Circle fitting of the edges of the retina. (c) Angle between the center of the retinal specialization and the nasal axis of the retina. The gray dot represents the center of the retina and the black dot, the center of the retinal specialization. (d) Distance from the center of the retina to the center of the retinal specialization (2.62). This distance is divided by the radius of the circle (10.65) to obtain a standardized distance of the retinal specialization to the center of the retina (0.25).

Figure 1

(a) Topographic map of the retinal ganglion cell distribution of the California Towhee Pipilo crissalis (Fernández-Juricic, Gall, et al., 2011). Shown are iso-density lines (connecting areas of the retina with the same cell density). (b) Circle fitting of the edges of the retina. (c) Angle between the center of the retinal specialization and the nasal axis of the retina. The gray dot represents the center of the retina and the black dot, the center of the retinal specialization. (d) Distance from the center of the retina to the center of the retinal specialization (2.62). This distance is divided by the radius of the circle (10.65) to obtain a standardized distance of the retinal specialization to the center of the retina (0.25).

Cartesian coordinates to establish the position of the retinal specialization in the retina. The coordinates consist of two linear distances (x- and y-coordinates) of both positive and negative values, depending on whether the position of the specialization is on the dorsal, ventral, nasal, or temporal sides of the retina.

Figure 2

Cartesian coordinates to establish the position of the retinal specialization in the retina. The coordinates consist of two linear distances (x- and y-coordinates) of both positive and negative values, depending on whether the position of the specialization is on the dorsal, ventral, nasal, or temporal sides of the retina.

(a) Example of the cell density points at the intersection of the iso-density lines along the nasal-temporal and dorsal-ventral vectors crossing the center of the retinal specialization. Notice that the line extends into the radial cuts of the retina (see text for details). (b) Example of the 21 cell density sampling points along the nasal-temporal vector, which divided the sampling line into 20 even spaces. At each point, we measured the mean cell density value that it fell in. (c) Example of the plot of the mean cell density in each sampling point from the temporal periphery of the retina to the center of the retinal specialization. We fitted a line and used its slope as the rate of change in cell density from the retinal periphery to the retinal specialization.

Figure 3

(a) Example of the cell density points at the intersection of the iso-density lines along the nasal-temporal and dorsal-ventral vectors crossing the center of the retinal specialization. Notice that the line extends into the radial cuts of the retina (see text for details). (b) Example of the 21 cell density sampling points along the nasal-temporal vector, which divided the sampling line into 20 even spaces. At each point, we measured the mean cell density value that it fell in. (c) Example of the plot of the mean cell density in each sampling point from the temporal periphery of the retina to the center of the retinal specialization. We fitted a line and used its slope as the rate of change in cell density from the retinal periphery to the retinal specialization.

Example of how to determine the mean cell density for each of the 21 sampling points. Shown are the first 13 and the last sampling points for the sake of clarity. Distances were scaled to mm to fit the scale provided in the topographic maps. Open circles represent the iso-density lines, and solid circles are the evenly spaced sampling points. The mean RGC density is an average of the RGC range between two iso-density lines. The edges of the retina are marked with sampling point 1 (0.00 mm) and 21 (12.28 mm). Sampling point 13 is the point that falls along the vector prior to crossing over the peak cell density of the retinal specialization. See explanation of the different steps (a through f) in the text.

Figure 4

Example of how to determine the mean cell density for each of the 21 sampling points. Shown are the first 13 and the last sampling points for the sake of clarity. Distances were scaled to mm to fit the scale provided in the topographic maps. Open circles represent the iso-density lines, and solid circles are the evenly spaced sampling points. The mean RGC density is an average of the RGC range between two iso-density lines. The edges of the retina are marked with sampling point 1 (0.00 mm) and 21 (12.28 mm). Sampling point 13 is the point that falls along the vector prior to crossing over the peak cell density of the retinal specialization. See explanation of the different steps (a through f) in the text.

Scatterplot of the discriminant functions (canonical axis scores) showing the discrimination of the three types of retinal specializations (fovea, area, and visual streak) for terrestrial vertebrates. We used two approaches, (a) linear and (b) nonlinear, to quantify cell density gradients (details in the text). Only two canonical axis scores were computed in each case. RS, retinal specialization.

Figure 5

Scatterplot of the discriminant functions (canonical axis scores) showing the discrimination of the three types of retinal specializations (fovea, area, and visual streak) for terrestrial vertebrates. We used two approaches, (a) linear and (b) nonlinear, to quantify cell density gradients (details in the text). Only two canonical axis scores were computed in each case. RS, retinal specialization.

Scatterplot of the discriminant functions (canonical axis scores) showing the discrimination of the three types of retinal specializations (fovea, area, and visual streak) for aquatic vertebrates. We used two approaches, (a) linear and (b) nonlinear, to quantify cell density gradients (details in the text). Only two canonical axis scores were computed in each case. RS, retinal specialization.

Figure 6

Scatterplot of the discriminant functions (canonical axis scores) showing the discrimination of the three types of retinal specializations (fovea, area, and visual streak) for aquatic vertebrates. We used two approaches, (a) linear and (b) nonlinear, to quantify cell density gradients (details in the text). Only two canonical axis scores were computed in each case. RS, retinal specialization.

Topographic maps of terrestrial vertebrates that were misclassified by the DFAs considering different retinal traits (see text for details). Two approaches were used (linear and nonlinear) for the classification. Scientific names are presented in Appendix 1. RS, retinal specialization.

Table 2

Topographic maps of terrestrial vertebrates that were misclassified by the DFAs considering different retinal traits (see text for details). Two approaches were used (linear and nonlinear) for the classification. Scientific names are presented in Appendix 1. RS, retinal specialization.

Topographic maps of aquatic vertebrates that were misclassified by the DFAs considering different retinal traits (see text for details). Two approaches were used (linear and nonlinear) for the classification. Scientific names are presented in Appendix 1. RS, retinal specialization.

Table 3

Topographic maps of aquatic vertebrates that were misclassified by the DFAs considering different retinal traits (see text for details). Two approaches were used (linear and nonlinear) for the classification. Scientific names are presented in Appendix 1. RS, retinal specialization.